Question

In a class of 60 students, 30 like cricket, 20 like football, and 10 like tennis. The number of students who like only tennis and cricket is twice that of those who like all the three sports.

The number of students who like only tennis is twice that of those who like only tennis and cricket.

If at least one student likes all the three sports, then how many students like only tennis and football?

• A. 3
• B. 5
• C. 4
• D. 2

Answer 1

The correct option is A 3

Let's make a Venn diagram for the situation.

Number of students who like only tennis = 4x
Number of students who like only tennis and cricket = 2x
Number of students who like all three sports = x

Let the number of students who like only tennis and football be y.

So,
Total number of students who like tennis = 10

4x + 2x + x + y = 10
7x + y = 10

It is given that at least one student likes all the three sports.
So,
x $\ge$ 1

Let's put x = 1
$7\times 1+y=10$
$7+y=10$
$y=10-7=3$

Let's put x = 2
$7\times 2+y=10$
$14+y=10$
$y=10-14=-4$

The number of students cannot be negative.
So, x cannot take values greater than or equal to 2.
Hence, x = 1 and y = 3

Therefore, the number of students who like only tennis and football is 3.